Method for locating a device which is moved in a three-dimensional space

ABSTRACT

A method of location of a device includes a displacement law containing a corrective factor of a bias combined by an arithmetical operation with a measured variable, and particles, each particle being associated with a current value of the corrective factor. The current value of the corrective factor being constructed at each iteration on the basis of a previous current value of the corrective factor, computed during a previous iteration, to which is added a random variable drawn according to a predefined probability law. The current values of various particles are initialized, before the first iteration, to various initial values, and during each iteration, for each particle whose coordinates are updated with the aid of this displacement law, the value of the corrective factor in the displacement law is taken equal to this corrective factor&#39;s current value associated with the particle.

RELATED APPLICATIONS

Under 35 USC 119, this application claims the benefit of the Jun. 18,2014 priority date of French Application FR 1455575, the content ofwhich is herein incorporated by reference in its entirety.

FIELD OF INVENTION

The invention relates to a method of location of a device which isdisplaced inside a three-dimensional space. The subject of the inventionis also an information recording medium, an electronic unit and a devicefor the implementation of this method.

BACKGROUND

Such methods are particularly useful when a method of location of thedevice by GPS (“Global Positioning System”) is not possible. This is forexample often the case inside buildings.

Known methods of location use the measurements of an inertial platformhoused inside the device itself to measure its direction of displacementand the amplitude of its displacement in this direction from a previousposition. Among these known methods, some use particle filters toestimate the position of the device in the three-dimensionalenvironment. Accordingly, particle filters exploit the fact that thereexist predefined constraints on the displacements of the device insidethe three-dimensional environment. For example, a typical constraint isthat a displacement cannot pass through a wall.

Thus, these known methods of location typically comprise:

a) the provision of a map of the three-dimensional space and ofpredefined constraints on the displacements of the device in thisthree-dimensional space,b) the generation, by an electronic computer, of several distinctparticles, each particle being associated:

-   -   with coordinates coding its position on the map, and    -   with a weight representing the probability that the device is        situated at the site of this particle,        c) the reception of measurements representative of the direction        of displacement of the device and of the amplitude of this        displacement from its previous position, these measurements        being carried out by sensors onboard the displaced device,        d) the updating of the coordinates of the position of each        particle as a function of the measurements received during        step c) and of a predetermined displacement law for displacing        this particle from its previous position P^(i) _(k-1) to a new        position P^(i) _(k) in a manner correlated with the measured        displacement of the device, each displacement law comprising for        this purpose at least one first measured variable whose value is        dependent on the measurement of the direction of displacement        received during step        c) and a second measured variable whose value is dependent on        the measurement of the amplitude of this displacement received        during step c), and then        e) for each particle, if the latest displacement of this        particle from the position P^(i) _(k-i) to the position P^(i)        _(k) satisfies the predefined constraints, the increasing of the        weight associated with this particle with respect to the weights        of the particles whose latest displacement infringes these        predefined constraints,    -   the repetition of steps c) to e), and        f) the estimation of the position of the device on the basis of        the positions of the particles and of the weights associated        with these particles by allotting, during this estimation, more        importance to the positions of the particles associated with the        highest weights.

Such known methods of location of a device implementing a particlefilter are for example disclosed in:

-   -   patent applications WO 2012158441 and U.S. Pat. No. 8,548,738        B1,    -   in the article O. Woodman et al., “Pedestrian localization for        indoor environments”, ACM, 2008.

Such a method is also disclosed in detail in the thesis of J. Straub,

“Pedestrian indoor localization and tracking using a particle filtercombined with a learning accessibility map”, thesis, August 2010,Technical University of Munich. This thesis is downloadable at thefollowing address:

http://people.csail.mit.edu/jstraub/download/Straub10PedestrianLocalization.pdf.

Subsequently, this thesis is referenced through the term “Straub 2010”.

Prior art is also known from:

-   -   EP2519803A, and    -   Krach B. et al., “Cascaded estimation architecture for        integration of foot-mounted inertial sensors”, Position,        location and navigation symposium, 2008, IEEE/ION, Piscataway,        2008 May 5.

Under ideal conditions, these known methods make it possible toprecisely estimate the position of the device. However, in reality,there may exist a constant bias in the direction of displacement of thedevice and/or in the amplitude of displacement of this device in thisdirection. This bias may have very different origins. For example, itmay be caused by a bias in the measurements of one or more of thesensors of the inertial platform incorporated in the device. It may alsobe caused by an error in modeling the relation which links themeasurements of the inertial platform to the directions of displacementand to the amplitude of this displacement. Finally, it may also becaused by an incorrect positioning of the device with respect to itsdirection of displacement.

The presence of a systematic bias such as this greatly degrades theprecision of the estimation of the position of the device if it is notcorrected. To correct such a bias, it is necessary to know its value.Now, in most cases, this value of the bias is not known in advance.Ideally, it would therefore be necessary to undertake a priorcalibration phase to determine the value of the bias, and then use thisvalue of the bias to correct the estimation of the position. However,obliging the user to execute a prior calibration phase before launchingthe location of the device is in most cases undesirable, or indeed quitesimply impossible in certain cases such as for example when the biasevolves over time.

SUMMARY OF INVENTION

The invention is aimed at remedying this problem by proposing a methodof location of the device which is more precise even in the presence ofa bias in the direction of displacement or in the amplitude of thedisplacement of this device.

Its subject is therefore a method as claimed in claim 1.

By way of illustration, in the method hereinabove, first particles areassociated with a first initial value for the corrective factor andsecond particles are associated with a second initial value for thissame corrective factor. To understand the benefit of this method, it isassumed that the first initial value is close to the actual value of thebias to be corrected. Conversely, it is assumed that the second initialvalue is further from the actual value of the bias to be corrected.Thus, the values of the corrective factor which are associated with thefirst particles make it possible to compensate the bias more correctlyand therefore to estimate the displacement of the device more precisely,on the basis of the same measurements. Under these conditions, as theiterations of steps c) to e) proceed, the position of the secondparticles is further and further from the real position of the device.Conversely, the position of the first particles remains close to thereal position of the device. Consequently, it is very probable that adisplacement of a second particle will rapidly infringe one or more ofthe predefined constraints on the displacements in the three-dimensionalenvironment. Hence, as the iterations of steps c) to e) proceed, theweight of the second particles rapidly becomes less important than thatof the first particles. The determination of the position of the deviceis then done, on the basis of a certain number of iterations of thesesteps c) to e), by giving more importance to the positions of the firstparticles than to the positions of the second particles. But, thepositions of the first particles are obtained by compensating the biasmore correctly. Thus, the device position estimated with the aid of themethod hereinabove rapidly becomes more precise than if a method oflocation not correcting this bias were used. Moreover, this result isachieved with no prior calibration phase. Indeed, the value of thecorrective factor which makes it possible to compute the displacement ofa particle as precisely as possible is selected automatically as theiterations of steps c) to e) proceed and therefore at the same time asthe position of the device is estimated.

The embodiments of this method of location can comprise one or more ofthe additional characteristics of the dependent claims.

These embodiments of the method of location furthermore exhibit thefollowing advantages:

-   -   applying the corrective factor to the measured variable        corresponding to the amplitude of the displacement of the device        makes it possible to automatically correct a bias in the        amplitude of the displacement of this device;    -   applying the corrective factor to a measured variable        corresponding to the direction of the displacement of the device        makes it possible to automatically correct a bias in the        direction of displacement;    -   during the step of generating new particles, associating these        new particles with initial values for the corrective factor        which are close to the corrective factor's current values        associated with the particles which have not been eliminated        makes it possible to increase the precision of the estimation of        the value of the corrective factor and therefore of the position        of the device as the iterations of steps c) to e) proceed;    -   using, in the guise of predefined constraints, the existence of        obstacles which are impassable to the device in the        three-dimensional environment makes it possible to accelerate        the convergence of the method of location toward a precise        estimation of the position of the device;    -   dividing the map into several zones and associating with each of        these zones a list of identifiers of the impassable obstacles        contained inside this zone makes it possible to retain a simple        tiling of the map into several zones while being capable of        using impassable obstacles situated entirely inside these zones;    -   dividing the map into several zones and associating with each of        these zones the displacement law which makes it possible to        estimate with more precision the displacement of the device in        this zone than if another displacement law associated with        another zone were used makes it possible to increase the        precision of the estimation of the position of the device;    -   using a favored direction of displacement in a zone of the map        to increase or on the contrary decrease the weight associated        with a particle makes it possible to converge more rapidly        toward a precise estimation of the position of the device.

The subject of the invention is also an information recording mediumcomprising instructions for the execution of the above method oflocation, when these instructions are executed by an electroniccomputer.

The subject of the invention is also an electronic locating unit.

Finally, the subject of the invention is also a device directlytransportable by a pedestrian who is moving in displacement inside athree-dimensional space, this device comprising:

-   -   an inertial platform able to measure physical quantities        representative of the direction of displacement of this device        and of the amplitude of this displacement, and    -   the electronic locating unit hereinabove.

The invention will be better understood on reading the description whichfollows, given solely by way of nonlimiting example and while referringto the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a vertical sectional schematic illustration of a buildinginside which is implemented a method of location of a device;

FIG. 2 is a schematic illustration of a location device;

FIG. 3 is a schematic illustration of a map used to locate the device ofFIG. 2 in the building of FIG. 1;

FIG. 4 is a flowchart of a method of location implemented by the deviceof FIG. 2.

DETAILED DESCRIPTION

In these figures, the same references are used to designate the sameelements. Hereinafter in this description, the characteristics andfunctions that are well known to the person skilled in the art are notdescribed in detail.

FIG. 1 represents an assembly comprising a building 2, inside which apedestrian 4 can move freely by walking. The building 2 is divided intoseveral stories. Here, only a ground floor story 6 and a first story 8are represented. The stories are linked together by zones of change ofstory such as a staircase or an elevator. Each story comprises rooms andcorridors delimited by impassable walls which the pedestrian 4 cannotcross. The pedestrian 4 can enter a room only by passing through a door.Here, the interior of a room can also comprise obstacles which areimpassable to the pedestrian 4 such as, for example, pillars or otherconstruction elements of the building 2.

To aid the pedestrian 4 to locate themself inside the building 2, thelatter transports a location device 10 directly in their hand. Thedevice 10 is capable of locating itself on a map of the building 2without recourse to sensors other than those which it comprisesinternally. In particular, the device 10 can chart its position insidethe building 2 without using a navigation system calling upon externalcharting beacons implanted in the environment of the building 2. Theseexternal beacons can be satellites or radio wave emitters fixed to thebuilding 2. In particular, the device 10 can chart its position withoutusing a GPS system (“Global Positioning System”).

FIG. 2 represents the device 10 in greater detail. The device 10comprises an electronic locating unit 11. This unit 11 comprises amemory 12 as well as a programmable electronic computer 14 capable ofexecuting instructions recorded in the memory 12. For this purpose, thememory 12 comprises the instructions necessary for executing the methodof FIG. 4. Moreover, the memory 12 comprises a map 16 of the building 2.This map is described in greater detail with reference to FIG. 3.

The device 12 also comprises an inertial platform 17. The inertialplatform 17 transmits to the computer 14, by way of an informationtransmission bus 19, measurements of the direction in which the device10 is moving and of the amplitude of the displacement in this directionfrom the latest logged position of this device 10. For this purpose, forexample, the inertial platform 17 comprises a three-axis accelerometer18, a gyrometer 19 and a three-axis magnetometer 20. Here, the inertialplatform 17 also comprises a barometer 21 for measuring the altitude ofthe device 10.

The device 10 is equipped with a screen 24 making it possible to displaya graphical representation 26 of the map 16 and, on this graphicalrepresentation, a point PA representing the current position of thedevice 4 inside the building 2. This point PA is therefore situated inthe graphical representation 26 at the site of the map 16 correspondingto the current position of the device 10 and therefore of the pedestrian4.

For example, the device 10 is a smartphone or an electronic tabletprogrammed to execute the method of FIG. 4.

FIG. 3 graphically represents the content of the map 16 for the story 8of the building 2. What will now be described in respect of the story 8of the building 2 applies to each story of this building and to theground floor story 6.

The map 16 comprises several zones 30 to 35 whose juxtaposition coversthe entire area of the story 8. These zones are parallel to the floor ofthe story and contained in one and the same plane called the “plane ofthe story”. This plane of the story is typically horizontal.

The zones 30 to 35 are contiguous and do not overlap. However, toincrease the readability of FIG. 3, the zones 30 to 35 are representedas overlapping but, in reality, this is not the case. Thus, here, eachportion of the periphery of each zone is common with at most one portionof the periphery of another different zone.

Conventionally, the edges of each zone are situated at the site of anobstacle which is impassable to the pedestrian 4 such as a wall.However, here, one and the same zone can encompass several rooms of thebuilding 2. This is for example the case for the zone 33 which surroundsa room 40 and another smaller room 42. In FIG. 3, the periphery of eachroom is delimited by walls represented by thin lines. Moreover, eachroom comprises at least one opening for accessing the interior of thisroom. In FIG. 3, the openings are situated between the wall ends markedby points. An opening is typically a door.

A zone can also encompass obstacles situated in the interior of a roomwhich are impassable to the pedestrian 4. For example, an impassableobstacle is an interior partition or a pillar or any other element ofthe building 2 which the pedestrian 4 cannot cross. Such a zone isillustrated by the zone 31 which comprises two partitions 44 and 46situated inside a room 48.

Here, each zone is a polygon. Hence, for each zone, the map 16 contains:

-   -   an identifier of this zone, and    -   the coordinates, in an XYZ frame, of the vertices of the polygon        delimiting this zone.

The XYZ frame is an orthogonal frame in which the X and Y directions arehorizontal and the Z direction is vertical. In this embodiment, eachzone is rectangular. Thus, only the coordinates of the two diagonallyopposite vertices of a zone are recorded in the map 16 so as toeconomize on memory.

For each zone, the map 16 also comprises:

-   -   a list of identifiers of just the impassable obstacles situated        inside this zone or on the periphery of this zone,    -   an identifier of a law of displacement inside this zone, and    -   optionally, a favored direction of displacement.

The position and the dimensions of each impassable object are here codedby a horizontal segment contained in the plane of the floor. Thus, eachobstacle identifier is associated with a pair of points E_(jd) andE_(jf). The points E_(jd) and E_(jf) mark, respectively, the start andthe end of the segment [E_(jd); E_(jf)], where j is the identifier ofthe impassable obstacle. The coordinates of the points E_(jd) andE_(jf), in the plane of the floor, are known and contained in the map16. Hence, for example, the zone 31 comprises eight obstacle identifiersIdO₁ to IdO₈. The identifiers IdO₁ to IdO₈ correspond, respectively, tothe segments [E_(a); E_(b)]; [E_(b); E_(c)]; [E_(c); E_(d)]; [E_(d);E_(f)]; [E_(f); E_(g)]; [E_(h); E_(i)]; [E_(j); E_(R)] and [E_(p);E_(m)]. The position of the points E_(a) to E_(m) is represented in FIG.3.

Each displacement law makes it possible to compute, on the basis of themeasurements of the inertial platform 17, at an instant t_(k), thedisplacement of a particle S¹ from a previous position P^(i) _(k-1) upto a new position P^(i) _(k). This displacement is directly correlatedwith that of the device 10. Typically, this displacement between thepositions P^(i) _(k-1) and P^(i) _(k) is identical or very close to thatof the device 10 between the instants t_(k-1) and t_(k). Subsequently,the superscript “i” is the identifier of the particle and the subscript“k” is the order number of the instant at which the direction and theamplitude of the displacement of the device 10 are measured.

The inertial platform 17 measures the angle θ_(k), in the plane of thestory, between the direction of displacement of the device 10 and the Xdirection. For this purpose, it is possible to use the measurements ofthe gyrometer 19 and of the magnetometer 20. Subsequently, the directionmeasured at the instant t_(k) is called “direction θ_(k)”.

The inertial platform 17 is also capable of providing a physicalquantity representative of the amplitude I_(k) of the displacement ofthe device 10 in the direction θ_(k) between the instants t_(k-1) andt_(k). For this purpose, it is possible to integrate the measurement ofthe accelerometer 18 between the instants t_(k-1) and t_(k) and, if themeasurement is zero, retain the previous measured speed v_(k-1).However, in the case of a pedestrian who is walking on a horizontalfloor, to obtain a more precise estimation of the amplitude l_(k), thecomputer 14 detects on the basis of the measurements of theaccelerometer 18 the instant at which a foot of the pedestrian 4 comesinto contact with the floor. On the basis of these successive instants,the computer 14 computes a frequency f_(k) of the footsteps of thepedestrian 4. Next, the amplitude I_(k) of the displacement of thepedestrian 4 in the direction θ_(k) is computed by using the followingfootstep model: I_(k)=Af_(k)+BT+C, where A, B, C and T are constantcoefficients independent of the measurements of the inertial platform17. Moreover, the coefficients A, B and C are coefficients which areindependent of the morphological characteristics of the pedestrian. Onthe other hand, the coefficient T must be chosen equal to the height ofthe pedestrian 4. By default, the coefficient T is taken equal to themean height of a human being, for example 1.78 m. The speed v_(k) ofdisplacement of the device 10 between the instants t_(k-1) and t_(k) isobtained with the aid of the following relation: v_(k)=I_(k)/Δt, whereΔt is the duration of the time interval between t_(k-1) and t_(k).Typically, Δt is chosen equal to the duration of a footstep of thepedestrian 4.

Thus, when the pedestrian 4 moves by walking on the floor of the story8, a displacement law is given by the following relations:

x ^(i) _(k) =x ¹ _(k-1) +v _(k)×Δt×cos θ_(k);

y ^(i) _(k) =y ^(i) _(k-1) +v _(k) ×Δt×sin θ_(k),

where (x^(i) _(k), y^(i) _(k)) and (x^(i) _(k-1), y^(i) _(k-1)) are thecoordinates, in the plane of the floor, of the positions P^(i) _(k) andP^(i) _(k-1) of the particle S^(i).

In the case of a method of location of the device 10 implementing aparticle filter, it is beneficial to explore the largest possible numberof trajectories with the particles. Thus, conventionally, thedisplacement of each particle is disturbed in a random manner. Forexample, accordingly, the usable displacement law is the following:

x ^(i) _(k) =x ^(i) _(k-1) +v _(k) ×Δt×cos θ_(k)+μ^(i) _(x);

y ^(i) _(k) =y ^(i) _(k-1) +v _(k) ×Δt×sin θ_(k)+μ^(i) _(y);

where μ^(i) _(k) μ^(i) _(y) are random variables.

At each instant t_(k) and for each particle S^(i), the values of thesevariables μ^(i) _(x) and μ^(i) _(y) are randomly drawn as a function ofa predefined centered probability law, that is to say characterized by azero mathematical expectation. Thus, the mean of the values of eachrandom variable μ^(i) _(x) and μ^(i) _(y) at the various successiveinstants t_(k) tends to zero as k increases. For example, thispredefined probability law is the same for the random variables μ^(i)_(x) and μ^(i) _(y) and for all the particles S^(i). Subsequently, it isdenoted Lp_(xy). This law Lp_(xy) is characterized by a predeterminedstandard deviation σ_(xy). Here, the standard deviation a_(xy) isconstant and independent of the measurements of the inertial platform 17for an updating at each footstep. For example, the standard deviationσ_(xy) is greater than 5 cm or 10 cm and, preferably, less than 35 cm.For example, the law Lp_(xy) is a uniform distribution or a Gaussiandistribution.

In reality, there may also exist a measurement bias, called thedirection bias, in the measurement of the direction θ_(k). Such adirection bias may originate from a defect in the sensors of theinertial platform 17. This direction bias may also be caused by the factthat the pedestrian 4 rotates the device 10 in a horizontal plane. In asimilar manner, there may also exist a measurement bias, called here thefootstep bias, in the measurement of the amplitude l_(k) of thedisplacement of the device 10. This footstep bias may originate from adefect of the sensors of the inertial platform. In the example describedhere, it may also originate from a modeling error and more preciselyfrom an error with respect to the default value of the coefficient T inthe footstep model. Indeed, the actual height of the pedestrian 4 isunknown. Thus, if the pedestrian 4 is much shorter or much taller than1.78 m, this introduces a systematic footstep bias in the measurement ofthe amplitude I_(k). Typically, these biases are constant at least overa time interval that is long enough to be able to estimate them andcorrect them as described subsequently.

Here, to compensate and correct these direction and footstep biases, thedisplacement law used integrates corrective factors, respectively σ^(i)and ε^(i), associated with each particle S^(i). For example, thedisplacement law is given by the following relations:

x ^(i) _(k) =x ^(i) _(k-1) +v _(k) ×Δt×(1+ε^(i) _(k))×cos(θ_(k)+α^(i)_(k))+μ^(i) _(x);

y ^(i) _(k) =y ^(i) _(k-1) +v _(k) ×Δt×(1+ε^(i) _(k))×sin(θ_(k)+α^(i)_(k))+μ^(i) _(y);

ε^(i) _(k)=ε^(i) _(k-1)+μ^(i) _(ε;)

α^(i) _(k)=α^(i) _(k-1)+μ^(i) _(α);

where:

-   -   ε^(i) _(k) and ε^(i) _(k-1) are the values, respectively at the        instants t_(k) and t_(k-1), of the corrective factor ε^(i) used        to correct the footstep bias, and    -   α^(i) _(k) and α^(i) _(k-1) are the values, respectively at the        instants t_(k) and t_(k-1), of the corrective factor α^(i) used        to correct the direction bias,    -   μ^(i) _(ε) and μ^(i) _(α) are random variables.

The random variables μ^(i) _(ε) and μ^(i) _(α) are used for the samereasons and in the same manner as the variables μ^(i) _(x) and μ^(i)_(y) introduced previously. Thus, a new value of the variables μ^(i)_(ε) and μ^(i) _(α) is randomly drawn at each new instant t_(k) and foreach particle S^(i) as a function, respectively, of a predefinedprobability law Lp_(ε) and of a predefined probability law Lp_(α).Typically, these laws Lp_(ε) and Lp_(α) are the same for all theparticles S^(i). Here, the mathematical expectations of the laws Lp_(ε)and Lp_(α) are equal to zero. Consequently, just as for the randomvariables μ^(i) _(x) and μ^(i) _(y), the mean of the values of eachrandom variable μ^(i) _(ε) and μ^(i) _(α) at the various successiveinstants t_(k) tends to zero as k increases.

Moreover, the function of the variables μ^(i) _(ε) and μ^(i) _(α) isonly to slightly disturb the previous values ε^(i) _(k-1) and α^(i)_(k-1) of the corrective factors ε^(i) and α^(i) so that the values ofthe corrective factors ε^(i) and α^(i) remain stable over time. For thispurpose, the standard deviations σ_(ε) and σ_(α), respectively, of thelaws Lp_(ε) and Lp_(α) do not allow a fast variation of the values ofthe corrective factors ε^(i) and α^(i). Here, for this purpose, thestandard deviation σ_(ε) is chosen sufficiently small for the ratioΣσ_(εk)/T to be less than 10%/s and, preferably, less than 5%/s or 1%/s,where:

-   -   σ_(εk) is the standard deviation of the law Lp, during the k-th        iteration of step 96,    -   Σσ_(εk) is the sum of the standard deviations σ_(εk) between the        q-th iteration and the p-th iteration of step 96, where q is an        integer strictly less than p,    -   T is the duration in seconds of the time interval which has        elapsed between the q-th 15 and the p-th iteration of step 96.

Step 96 is the step during which the coordinates of the particle S^(i)are updated. This step is described in greater detail with reference toFIG. 4. Here, the standard deviation a, is constant. Thus, the previousratio can also be written: (p-q)σ_(ε)/T. In this case, whatever p and q,the ratio is constant. The difference p-q is generally large enough tocover a time period of greater than 1 s or 4 s and, generally, less than10 min or 5 min or 1 min. For example, this difference between p and qis constant whatever p.

In a similar manner, the standard deviation σ_(α) is chosen sufficientlysmall for the ratio Σσ_(αk)/T to be less than 10°/s and, preferably,less than 5°/s or 1°/s, where:

-   -   σ_(αk) is the standard deviation of the law Lp_(a) during the        k-th iteration of step 96,    -   Σσ_(αk) is the sum of the standard deviations σ_(αk) between the        q-th iteration and the p-th iteration of step 96, where q is an        integer strictly less than p,    -   T is the duration in seconds of the time interval which has        elapsed between the q-th and the p-th iteration of step 96.

Here, the standard deviation a_(a) is also constant. Thus, the previousratio can also be written: (p-q)σ_(α)/T.

Just as for the variables μ^(i) _(x) and μ^(i) _(y), the variables μ^(i)_(ε) and μ^(i) _(α) make it possible to explore a large number ofpossible values for the corrective factors ε^(i) and α^(i).

The displacement law described hereinabove is subsequently called thefirst 35 displacement law. This first displacement law operates in mostsituations where the pedestrian 4 walks on a horizontal ground. On theother hand, in certain particular cases, there exist other more precisedisplacement laws. For example, the zone 35 is a stairwell comprising astaircase 50. In this zone 35, the length of the footsteps of thepedestrian 4 is imposed by the depth L_(ri), of the stairs of thisstaircase 50. Thus, in the zone 35, it is preferable to use a seconddisplacement law. Here, this second displacement law is identical to thefirst displacement law except that the product v^(i) _(k)×Δt×(1+ε^(i)_(k)) is replaced with the measured variable n^(i) _(k). The variablen^(i) _(k) is given by the following relation: n^(i) _(k)=(Ent(|z^(i)_(k)−z^(i)k-1|/H_(m)))×L_(m), where:

-   -   z^(i) _(k-1) and z^(i) _(k) are the heights of the device 10        measured by the inertial platform 17 at the instants t_(k-1) and        t_(k), respectively,    -   H_(m) is the constant height of a stair of the staircase 50,    -   is the depth of a stair of the staircase 50,    -   |z^(i) _(k)−z^(i) _(k-1)| is the function which returns the        absolute value of the difference between Z^(i) _(k) and z^(i)        _(k-1), and    -   Ent ( . . . ) is the function which returns the integer part of        |z^(i) _(k)−z^(i) _(k-1)|/H_(m).

Here, it is assumed that the height H_(m) and the depth L_(m) are knownin advance and recorded in the map 16.

The values of the measured variables z_(k) and z_(k)-₁ are obtained,typically, on 15 the basis of the measurements of the barometer 21.Here, only the zone 35 is associated with this second displacement law.All the other zones of the story 8 are associated with the firstdisplacement law.

Inside the building 2, there exist zones such as the zones 30, 31, 33and 34 in which the pedestrian 4 can move freely in all directions.Stated otherwise, in these zones, it is considered that all thedirections of displacement are equiprobable. In this case, these zonesare devoid of favored direction of displacement. Conversely, there existzones of the building 2 where not all the directions of displacement areequiprobable. For example, the zone 32 is a long corridor parallel tothe X direction. In this zone 32, the most probable directions ofdisplacement for a pedestrian are parallel to the X direction. Indeed,it is less probable for the pedestrian 4 to move transversely to thelongitudinal direction of the corridor. In this case, there is said tobe a favored direction of displacement in this zone 32. Here, eachfavored direction is coded by an angle y, in the plane of the floor,between this favored direction and the X direction. Moreover, in thisembodiment, an angular tolerance σ_(γ) is also associated with eachfavored direction. This angular tolerance is generally expressed indegrees or in radians. For example, in the case of the zone 32, theangle γ=0° and the angular tolerance σ_(γ)=±30°. In the embodimentdescribed here, the zone 35 is also associated with a favored directionfor ascending and descending the staircase 50. For this favoreddirection, the angle γ=90° and the angular tolerance σ_(γ) is equal to±20°.

The manner of operation of the device 10 will now be described withreference to the method of FIG. 4.

To locate the position of the device 10 inside the building 2, the unit11 implements a location algorithm known by the term “particle filter”.The manner of operation of a particle filter is well known. For example,the reader can refer to the prior art cited in the introduction of thispatent application and, in particular, to Straub 2010. Thus,subsequently, only the new specifics of implementation of this algorithmare described in detail. In particular, the management of the changes ofstories is carried out, for example, as described in Straub 2010.

The method starts with a step 90 when location of the device 10 istriggered. For example, location is triggered manually by the pedestrian4 by interacting with the man-machine interface of the device 10. Thecomputer 14 then generates an initial assembly of N₀ particles S^(i),where i is an identifier of the particle making it possible todistinguish it from among the set of other particles generated. Thenumber N₀ of particles S^(i) depends in particular on the initialknowledge that one has about the position of the device 10 in thebuilding 2 and the area of this building. Typically, N₀ is greater than10 or 100. N₀ is also generally less than 5000 or 1000. Each particleS^(i) is initially associated:

-   -   with an initial position P^(i) ₀ inside the building 2, this        position P^(i) ₀ comprising the coordinates x^(i) ₀, y^(i) ₀ and        z^(i) ₀ of the particle S^(i) in the XYZ frame,    -   with an initial value w^(i) ₀ of the weight w^(i) representing        the probability that the device 10 is situated at the site of        this particle S^(i) at the instant t₀,    -   with an initial value α^(i) ₀ for the corrective factor α^(i),        and    -   with an initial value ε^(i) ₀ for the corrective factor ε^(i).

During step 90, the initial position P^(i) ₀ and the initial valuesw^(i) ₀, α^(i) ₀ and ε^(i) ₀ are initialized. Numerous schemes forinitializing the positions P^(i) ₀ and the values w^(i) ₀ of eachparticle are known. For example, if the initial position of the device10 is known to within plus or minus 1 m, the values P^(i) ₀ of all theparticles S^(i) are drawn at random inside a circle centered on theknown position and of radius equal to 1 m. It is also possible to takeeach value w^(i) ₀ equal to 1/N₀, where N₀ is the initial number ofparticles generated.

Each value α^(i) ₀ is drawn at random in such a way that thedistribution of the initial values α^(i) ₀ follows a predeterminedprobability law Lp_(α0) such as a uniform or Gaussian or otherdistribution. The law Lp_(α0) is generally not the same as the lawLp_(α) which is used to obtain the values of the random variable μ^(i)_(α). It is the a priori knowledge that one has about the distributionof the direction bias which makes it possible to choose the probabilitylaw for the initial values α^(i) ₀ which most resembles the one observedin reality. For example, it is also this a priori knowledge about thedistribution of the direction biases which makes it possible to fix thevalue of the standard deviation σ_(α0) of the law Lp_(α0). For example,the standard deviation σ_(α0) is chosen equal to 360° if one has noinformation about the direction bias. In another example, the standarddeviation σ_(α0) is chosen less than 45° if one has a little informationabout the direction bias. In contradistinction to the case of theprevious random variables, this probability law Lp_(cio) does notnecessarily have a zero mean.

Each initial value ε^(i) ₀ is chosen as described previously for theinitial values α^(i) ₀ except that a predefined probability law Lp_(ε0)is used for the footstep bias, instead of the law Lp_(α0). Moreover, theprobability law Lp_(ε0) is not necessarily identical to the law Lp_(α0).Indeed, generally, the direction bias and footstep bias are notcorrelated. Typically, the standard deviation σ_(ε0) of the law Lp_(ε0)is equal 30% to within plus or minus 5% if one has no information aboutthe footstep bias. In another example, the standard deviation σ_(ε0) ischosen less than 20% if one has a little information about the footstepbias.

Thereafter, during a step 92, the inertial platform 17 transmits itsmeasurements to the computer 14 which receives them. On the basis ofthese measurements, the computer 14 computes the speed v_(k) and theangle θ_(k) of the current displacement of the device 10 from its latestposition. Here, new measurements of the speed v_(k) and of the angleθ_(k) are computed each time that the computer detects that a foot ofthe pedestrian has just touched the floor.

During a step 94, the computer 14 identifies, for each particle S^(i),the zone inside which it is currently situated. Accordingly, for eachparticle S^(i), the computer compares the latest known position P^(i)_(k-1) of this particle with the periphery of each zone of the map 16.For example, in the case of rectangular zones aligned with the XYZframe, the computer 14 tests whether the following two inequalities aresatisfied: x_(Aj)≦x^(i) _(k-1)≦x_(BJ) and y_(AJ)≦y^(i) _(k-1)≦y_(Bj),where:

-   -   the subscript j is an identifier of the zone of the map 16        making it possible to distinguish it from the other zones,    -   x_(Aj) and y_(Aj) are the coordinates of that vertex of zone j        which is closest to the origin of the XYZ frame, and    -   x_(Bj) and y_(Bj) are the coordinates of that vertex of zone j        which is furthest from the origin of the XYZ frame.

If these two inequalities are satisfied, then the particle S^(i) belongsto zone j. Preferably, the computer 14 tests firstly whether theparticle S^(i) belongs to the same zone as that to which it belongedpreviously. If a particle S^(i) does not belong to any zone, then aparticular processing is triggered. For example, this particle iseliminated.

During a step 96, once the zone to which each particle S^(i) belongs hasbeen identified, each particle is displaced in a manner correlated withthe measured displacement of the device 10 from its previous positionP^(i) _(k-1) up to a new position P^(i) _(k). Accordingly, thecoordinates of each particle S^(i) are updated as a function:

-   -   of the latest measurements received from the inertial platform        17,    -   of the coordinates of the previous position P^(i) _(k-1) of this        particle, and    -   of the displacement law associated with the zone inside which        the particle S^(i) is situated.

The displacement law to be used is therefore that associated with thezone identified during step 94.

For example, if the particle S^(i) is situated inside one of the zones30 to 34, then the coordinates of the new position P^(i) _(k) areestablished using the first displacement law. On the other hand, if theparticle S^(i) is situated inside the zone 35, then the coordinates ofthe new position P^(i) _(k) are established using the seconddisplacement law.

At each new execution of step 96, the new values for the variables μ^(i)_(x), μ^(i) _(y), μ^(i) _(α) and μ^(i) _(ε) are randomly drawn with theaid of the laws Lp_(xy), Lp_(α), and Lp_(ε), respectively.

During a step 98, the computer 14 updates the weights w^(i) of eachparticle S^(i). More precisely, the computer 14 decreases the weightw^(i) of the particle S^(i) if its latest displacement from the positionP^(i) _(k-1) to the position P^(i) _(k) has infringed predefinedconstraints associated with the zone inside which it is situated.

Typically, for each particle S^(i), the computer here verifies thefollowing onstraints:

-   -   constraint 1): the segment [P^(i) _(k-1); P^(i) _(k)] must not        cross an impassable obstacle of the zone inside which this        particle S^(i) is situated;    -   constraint 2): the direction of the displacement from the        position P^(i) _(k-1) to the position P^(i) _(k) complies with        the favored direction of displacement associated with the zone        inside which the particle S^(i) is situated.

Generally, here a constraint on the displacement of the particle S^(i)is defined as being a condition which, if it is satisfied by theparticle S^(i), is used to increase the weight w^(i) of this particleS^(i) with respect to the weight of the particles which do not satisfythis condition. Conversely, if this condition is not satisfied by theparticle S_(i), then it is used to decrease the weight w^(i) of thisparticle S^(i) with respect to the weights of the particles whichsatisfy this condition.

To evaluate the constraint 1), for each particle S^(i), the computer 14searches for whether there exists an intersection between the segment[P^(i) _(k-1); P^(i) _(k)] and each impassable obstacle of the zoneinside which the particle is situated. This zone was identified duringstep 94. This intersection search is carried out solely with theimpassable obstacles whose identifiers are contained in the listassociated with the identified zone. Here, since each obstacle is codedby a segment, this intersection search amounts to searching for anintersection between two segments.

If an intersection exists, then a very low or zero value is assigned tothe weight w^(i). A very low value is a value less than 0.2 or 0.1 forexample. In the converse case, the value of the weight w^(i) remainsunchanged.

If the zone inside which the particle S^(i) is situated is notassociated with a favored direction, then the constraint 2) is not usedto update the weight w^(i). In the converse case, the constraint 2) isused. To evaluate the constraint 2), the computer 14 computes a weightw^(i) _(θ) on the basis of the deviation between the direction measuredθ_(k) for the displacement of the particle S^(i) and the favoreddirection of the zone inside which it is situated. The value of theweight w^(i) _(θ) is all the larger the lower the angular deviationbetween the favored direction y and the direction of displacement fromthe position P^(i) _(k-1) to P^(i) _(k). Moreover, here, the value ofthe weight w^(i) _(θ) is established while taking account of thetolerance σ_(γ) associated with this favored direction. The value of theweight w^(i) _(θ) is therefore larger if the angular deviation betweenthe direction of displacement of the particle S^(i) and the favoreddirection lies in the tolerance margin defined by the value of σ_(γ)and, in the converse case, the value of the weight w^(i) _(σ) issmaller.

For example, here, the value of the weight w^(i) _(σ) is computed withthe following relation: w^(i) _(σ)=p×exp[(θ_(k)+α^(i) _(k)−γ)²/(2σ_(γ)²)], where p is a predefined constant coefficient. It will be noted thatthe value α^(i) _(k) of the corrective factor α^(i) of the directionbias is also used to compute this weight w^(i) _(σ).

Thereafter, the value of the weight w^(i) is taken equal to its previousvalue multiplied by the value of the weight w^(i) _(θ) thus obtained.

During a step 100, the computer 14 undertakes the normalization of theweights w^(i) of all the particles S^(i) so that the sum of all theseweights is equal to one. For example, the computer 14 computes the sum Wof all the weights w^(i) and then divides each weight w^(i) by the sumW.

During a step 102, the computer 14 re-samples the particles S^(i). Thisre-sampling step consists in eliminating the particles whose weightsw^(i) have become too low to replace them with particles associated withparameters whose weights are higher.

Numerous re-sampling techniques are known. For example, here, we apply25 the SIR (Sequential Importance Resampling) scheme described in thefollowing book: B. Ristic, S. Arulampalam, N. Gordon, “Beyond the KalmanFilter, particle filter for tracking applications”, Artech House, 2004.

To summarize, this re-sampling scheme firstly consists in classing theparticles into two groups: the particles to be regenerated, that is tosay all the particles whose weight is below a predetermined thresholdand the surviving particles, that is to say the other particles.

Thereafter, for each particle to be regenerated, the computer 14eliminates the old particle and then generates a new particle to replaceit. To generate a new particle, the computer 14 randomly draws aparticle from the group of surviving particles. This chance drawing iscarried out preferably in such a way that the probability of being drawnis proportional to the weight of the surviving particle.

Thereafter, the position P^(i) _(k) and the values α^(i) _(k) and ε^(i)_(k) of the drawn surviving particle are assigned to the new generatedparticle. During this step, preferably, the computer adds a randomdisturbance on the position and on the values of the corrective factorsby using, for example, the random variables μ_(x), μ_(y), μ_(α) andμ_(ε). However, these disturbances are calibrated in such a way that thevalues α^(i) _(k) and ε^(i) _(k) assigned to the generated particleremain very close to the current values for the corrective factorsassociated with the surviving particle drawn. Typically, the mean of thevalues α^(i) _(k) which are assigned to the generated particles iscloser to the mean of the values α^(i) _(k) of the surviving particlesthan to the mean of the values α^(i) _(k) of the eliminated particles.The same holds for the values ε^(i) _(k) assigned to the generatedparticles.

A new weight is also assigned to each generated particle and,optionally, to the surviving particle from which it arises.

During a step 104, the computer 14 estimates the position PA of thedevice 10 on the basis of the positions P^(i) _(k) and of the weightsw^(i) of all the particles S^(i). Numerous schemes are possible fordoing this. For example, the position PA is taken equal to that of theparticle S^(i) having the highest weight w^(i). In another embodiment,the position PA is taken equal to the mean of the positions P^(i) _(k)of the particles S^(i) on weighting each position P^(i) _(k) by theweight w^(i). Another scheme is also described in application WO2012158441.

Finally, during a step 106, a point is displayed at the position PA onthe graphical representation 26 of the map 16 to indicate to thepedestrian 4 his position on this map and therefore his position insidethe building 2.

Steps 92 to 106 are repeated in a loop. As these iterations proceed, theprecision of the estimation of the position of the device 10 increasessince only the most probable positions P′_(k) are retained.

In parallel with step 104, during a step 108, the computer 14 computesan estimation E_(α) of the direction bias and an estimation E_(ε) of thefootstep bias on the basis, respectively, of the current values α^(i)_(k) and ε^(i) _(k) of the particles S^(i). For example, the estimationE_(α) is taken equal to the mean of the current values α^(i) _(k) of allthe particles S^(i). In a similar manner, the value of the estimation E,is taken equal to the mean of the current values ε^(i) _(k) of all theparticles S^(i).

The precision of the estimations E_(α) and E_(ε) increases as therepetitions of steps 92 to 106 proceed. Indeed, it is very probable thatthe particle S^(i) associated with an incorrect current value for thecorrective factor α^(i) or ε^(i) will rapidly infringe the constraintsevaluated during step 98. Hence, the particles S^(i) associated withincorrect current values for the corrective factors are preferablyeliminated during step 102. Thus, as the iterations of steps 92 to 106proceed, the particles S^(i) associated with 35 correct current valuesfor the corrective factors are preferably selected as survivingparticles during step 102. Hence, the estimations E_(α) and E_(ε)converge toward the actual values of the direction bias and the footstepbias.

Moreover, since the values of the corrective factors α^(i) and ε^(i)converge toward the actual values of the direction and footstep biasesas the iterations of steps 92 to 106 proceed, the corrective factorscorrect these direction and footstep biases more and more precisely.Hence, the presence of these corrective factors in the displacement lawmakes it possible to substantially increase the precision of theestimation of the position PA even in the presence of such direction andfootstep biases.

The estimations E_(ε) and E_(α) can be displayed on the screen 24 orused by other applications to correct the direction and footstep biases.

Numerous other embodiments are possible. For example, certain moresophisticated sensors provide a mean value of the variable measured atan instant k as well as a standard deviation in this measurement (seefor example Straub 2010). In this case, the measured values of the angleθ_(k) and of the amplitude I_(k) are obtained by drawing the values atrandom using a Gaussian probability law whose mean and standarddeviation are equal to those transmitted by the sensors. This makes itpossible in particular to take the measurement noise into account.

What was described previously in the particular case where it is apedestrian who directly carries the device 10 may also be adapted toother situations. For example, the device 10 can be fixed on a trolleypushed by the pedestrian. In this case, the speed v_(k) is obtained byintegrating the acceleration measured by the trolley. Another solutionconsists in detecting the frequency of the impacts which occur each timea wheel of the trolley rolls over a join between two flagstones of aground 20 pavement. The method of location described also applies to thecase where the device 10 is transported by a motorized robot which moveswithout the aid of the pedestrian 4. In this case, the amplitude of thedisplacement can be measured by measuring the number of wheelrevolutions of a driving wheel of the robot.

The method described above applies to any type of three-dimensionalspace where the device 10 can be displaced. For example, it may alsoentail a space situated outdoors and outside any building. For example,this method is useful to locate a person in a place where location byGPS or on the basis of telephonic relay is impossible.

Other ways of coding the constraints on the displacement of the device10 exist and are usable in the above method. For example, rather thanrecording the position of the walls, it is possible to record all thepossible paths. If the displacement of a particle does not follow one ofthese possible paths, then its weight is decreased. Such an embodimentis described in greater detail in application WO 2012158441 and inapplication U.S. Pat. No. 8,548,738. Rather than recording the positionof the walls, it is also possible to record the position of the doors.In the latter case, the weight of a particle is increased if the lattergoes from one room to another by passing through a door. Such anembodiment is described in greater detail in Straub 2010.

Other predefined constraints can be used to update the value of theweight w^(i). For example, if an approximate measurement of the positionof the device 10 is available by using other information, then theweight w^(i) is increased if the position P^(i) _(k) is close to thisapproximate position and, on the contrary, decreased if the positionP^(i) _(k) is far from this approximate position. For example, theapproximate position is obtained on the basis of the power of aradioelectric signal received by the device 10 and of the known positionin the XYZ frame of the emitter of this radioelectric signal. Forexample, the emitter is a Wi-Fi terminal.

Although the constraint consisting in testing the collision of aparticle with an impassable obstacle is, in practice, the one used mostoften, it is not absolutely necessary if there exist other predefinedconstraints such as those described above which can be used.

As a variant, step 100 of normalizing the weight w^(i) of the particlesS^(i) is omitted.

During the re-sampling of the particles, numerous other algorithms fordetermining the initial position of the regenerated particles are knownand may be used instead of that described above. For example, the KLD(Kullbak-Leibler-Divergence) algorithm can be used.

Likewise, other algorithms are possible for associating a new currentvalue α^(i) _(k) and ε^(i) _(k) with each regenerated particle. Each newvalue α^(i) _(k) is dependent on one or more of the values α^(i) _(k)associated with the particles which have not been eliminated and isindependent of the values α^(i) _(k) associated with the particles whichhave been eliminated. The same holds for the new value ε^(i) _(k).

In a simplified variant, the re-sampling step 102 is omitted. Even ifthe re-sampling is not undertaken, the method hereinabove makes itpossible to increase the precision of the location of the position ofthe device 10 since the weight w^(i) of each particle S^(i) associatedwith an incorrect current value α^(i) _(k) or ε^(i) _(k) decreases asthe iterations of steps 92 to 104 proceed.

Other schemes for determining whether a particle is situated inside azone are possible. For example, Straub 2010 describes an alternativescheme usable in the case of polygonal zones of more complicated shapethan a simple rectangle.

Shapes of zones other than polygons are possible. For example, a zonecan have the shape of a circle. In this case, the coordinates of itscenter and of its radius are recorded in the map 16. There is in realityno limitation on the shape of a zone as long as the coordinates of theperiphery of this zone can be determined in the XYZ frame.

The above method has been described in the particular case where eachzone is associated at one and the same time with impassable-obstacleidentifiers, a displacement law and a favored direction. However, it mayfrequently happen that the displacement law is the same for severalimmediately contiguous zones. For example, here, this is the case forzones 30 to 34 which are all associated with the first displacement law.In this case, it may be more beneficial to record in the map 16 severalstacked strata of zones for one and the same story. Each stratumcomprises at least one zone and, typically, a set of several zonescovering the entire area of the floor. The zones of one stratum aredistinguished from the zones of another stratum by the type of propertythat it associates with this zone. For example, a first stratumcomprises solely zones associated only with impassable-obstacleidentifiers. A second stratum comprises solely zones associated onlywith a respective displacement law. Finally, a third stratum comprisesonly zones associated solely with a favored direction. When such a stackof strata is applied to the story 8, the zones of the first stratum are,for example, identical to the zones 30 to 35 except that they compriseonly the identifiers of impassable obstacles. Here the second stratum islimited to two zones. One of them is identical to the zone 35 exceptthat it is solely associated with the second displacement law. The otherzone of this second stratum corresponds to the union of zones 30 to 34and is solely associated with the first displacement law. Here the thirdstratum comprises four zones. The first and second zones are identical,respectively, to zones 32 and 35 except that they are solely associatedwith a respective favored direction. The third zone corresponds to theunion of zones 30 and 31 and the fourth zone then corresponds to theunion of zones 33 and 34 which are not associated with any favoreddirection.

The manner of operation of the method of location with a map comprisingseveral strata is identical to that described above except that, foreach particle S^(i), the zone of each stratum inside which it issituated is identified. Thereafter, it is these zones inside which it issituated which make it possible to identify the displacement law to beused and the predefined constraints to be tested so as to update thevalue of its weight w^(i). The use of several strata of zones maysimplify the definition of these zones.

In another variant, one of these strata corresponds to an accessibilitymap such as described in Straub 2010 in chapter 5.1.2. However,preferably, the various contiguous boxes of the accessibility map ofStraub 2010 that are associated with the same value of the degree λ ofaccessibility are grouped together within one and the same zone.

Each zone can also be associated with additional predefined constraintsfor updating the weight w^(i) of the particles situated in this zone.For example, it is possible to associate with each zone a coefficientw_(a) of accessibility which represents the probability that apedestrian enters this zone. Thereafter, when updating the weight w^(i)of a particle SI situated in this zone, the weight w^(i) is taken equalto its previous value multiplied by this coefficient w_(a).

Other displacement laws are usable. For example, the standard deviationsσ_(α) and σ_(ε) are not necessarily constant. In this case, they areconstant over long durations and then modified for a brief time intervalbefore returning to their previous values. For example, solely duringthis brief time interval, the ratios Σσ_(εk)/T and/or Σσ_(αk)/T arepermitted to exceed the previously defined thresholds. Typically, thetemporary increasing of the values of the standard deviations σ_(α) andσ_(ε) is used to reinitialize the current values α^(i) _(k) and ε^(i)_(k). Generally, the values of the standard deviations σ_(α) and Σ_(ε)are constant for more than 90% of the time of use of the device 10 so asto prevent, during this 90% of the time, a fast variation of the valuesof the corrective factors ε^(i) and α^(i). It is possible to verify thatthe ratio Σσ_(εk)/T is maintained below a predetermined threshold overat least 90% of the time of use, for example, by taking the differencep-q equal to a constant. Thereafter, the ratio Σσ_(εk)/T is computed foreach value of p corresponding to an iteration of step 96 occurringduring this time of use. If at least 90% of the ratios thus computed arebelow the predetermined threshold, then this ratio is maintained belowthis predetermined threshold for more than 90% of the time of use. Thesame computation can be used for the ratio Σσ_(αk)/T. The time of use isfor example a period of continuous use of the device 10 without stoppingthe execution of the method of FIG. 4.

In another variant, the expectation of one of the probability lawsLp_(ε) or Lp_(α) is non-zero. This then introduces an additional biaswhich is added to the real bias. The current value ε^(i) _(k) or α^(i)_(k) can also be computed on the basis of a previous value other thanε^(i) _(k-1) or α^(i) _(k-1). For example, ε^(i) _(k) is computed on thebasis of the previous value ε^(i) _(k-n), where n is a constant strictlygreater than one. Thus, it is also possible to use the followingrelations to compute the current value of ε^(i) _(k): ε^(i) _(k)=(ε^(i)_(k-1)+ε^(i) _(k-2))/2+μ^(i) _(ε) or ε_(k)=ε^(i) _(k-2)+μ^(i) _(ε). Thesame thing applies to the computation of the current value α^(i) _(k).

Moreover, if it is known that the direction bias is zero or negligible,then the first and the second displacement laws are simplified byeliminating the corrective factor α^(i). Conversely, if it is known thatthe footstep bias is zero or negligible, then the first displacement lawis simplified by eliminating the corrective factor ε^(i). The correctivefactor remaining in the first displacement law is thereafter estimatedas described above with reference to FIG. 4. Conversely, it is possibleto add additional corrective factors to the first displacement law. Forexample, if the best possible value of the coefficient A in the footstepmodel of the first displacement law is not known precisely, it is thenpossible to use the following footstep model I_(k)=πAf_(k)+BT+C, where πis an additional corrective factor. The value of the factor π is thenestimated in the same manner as was described for the corrective factorsα^(i) and ε^(i). It will be noted that in the case of the correctivefactor Tr, the latter is a multiplicative factor and not a subtractivefactor, that is to say that it multiplies the measured variable f_(k).

Displacement laws other than those described above may be used. Forexample, a displacement law specifically adapted to the displacement onan escalator or on a moving walkway or in an elevator can readily bedesigned and associated with the zone comprising this escalator, thismoving walkway or this elevator. Moreover, if there exists a measurementbias in these particular zones, then it is desirable to introduce acorrective factor into the displacement law to compensate thismeasurement bias. If, initially, the value of this corrective factor isnot known, then this value is estimated in the same manner as wasdescribed for the corrective factors α′ and ε^(i).

Step 106 or 108 is not necessarily carried out after each iteration ofsteps 92 to 104. For example, these steps are carried out only one timeout of two.

The previous embodiments have been described in the particular casewhere all the processings to determine the position PA are carried outby the computer 14 of the device 10. As a variant, these processings aredistributed over several distinct computers. One of these distinctcomputers can be that of a computer server mechanically independent ofthe device 10. For example, the device 10 transmits the measurements tothis server and this server determines the position PA and then returnsthe position PA determined to the device 10 which displays it on itsscreen 24. In this case, the map 16 is also recorded in the memory ofthis server.

The selection of a specific displacement law as a function of the zonein which the particle is situated can be implemented independently ofthe other characteristics of the method of FIG. 4. In particular, thisselection of the displacement law can be implemented independently ofthe use of corrective factors such as the factors α^(i) and ε^(i) and/orindependently of the use, in the guise of predefined constraints, of thefavored directions of displacement.

Likewise, the use of favored directions of displacement associated withzones can also be implemented independently of the other characteristicsof the method of FIG. 4. In particular, the use, in the guise ofpredefined constraints, of the favored directions of displacement can beimplemented independently of the use of corrective factors such as thefactors α^(i) and ε^(i) and/or independently of the selection of thedisplacement law as a function of the zone inside which the particle issituated.

1. A method of location of a device which is displaced inside athree-dimensional space, the method comprising: a) the provision of amap of the three-dimensional space and of predefined constraints on thedisplacements of the device in this three-dimensional space, b) thegeneration, by an electronic computer, of several distinct particles,each particle being associated: with coordinates coding its position onthe map, and with a weight representing the probability that the deviceis situated at the site of this particle, c) the reception ofmeasurements representative of the direction of displacement of thedevice and of the amplitude of the displacement from its previousposition, the measurements being carried out by sensors onboard thedisplaced device, d) the updating of the coordinates of the position ofeach particle as a function of the measurements received during step c)and of a predetermined displacement law for displacing this particlefrom its previous position P^(i) _(k-1) to a new position P^(i) _(k) ina manner correlated with the measured displacement of the device, eachdisplacement law comprising for this purpose at least one first measuredvariable whose value is dependent on the measurement of the direction ofdisplacement received during step c) and a second measured variablewhose value is dependent on the measurement of the amplitude of thisdisplacement received during step c), and then e) for each particle, ifthe latest displacement of the particle from the position P^(i) _(k-1)to the position P^(i) _(k) satisfies the predefined constraints, theincreasing (98) of the weight associated with this particle with respectto the weights of the particles whose latest displacement infringesthese predefined constraints, the repetition of steps c) to e), and f)the estimation of the position of the device on the basis of thepositions of the particles and of the weights associated with theseparticles by allotting, during this estimation, more importance to thepositions of the particles associated with the highest weights, wherein:the displacement law also comprises a corrective factor of a biascombined by an arithmetical operation with one of the measuredvariables, and each particle is also associated with a current value ofthe corrective factor, the current value of the corrective factor beingconstructed at each iteration of step d) on the basis of a previouscurrent value of this corrective factor, computed during a previousiteration of step d), to which is added a random variable drawnaccording to a predefined probability law, and the current values ofvarious particles being initialized, before the first execution of stepd), to various initial values, and during step d), for each particlewhose coordinates are updated with the aid of the displacement law, thevalue of the corrective factor in the displacement law is taken equal tothis corrective factor's current value associated with the particle. 2.The method as claimed in claim 1, in which the corrective factor is, inthe displacement law, added together or multiplied with the secondmeasured variable and the variation of the standard deviation σ_(ε) ofthe predefined probability law is maintained below 10% per second formore than 90% of the time of use of the method for locating the device,the variation of the standard deviation σ_(ε) being given by thefollowing ratio: Σσ_(εk)/T, where: σ_(εk) is the standard deviation ofthe predefined probability law during the k-th iteration of step d),Σσ_(εk) is the sum of the standard deviations σ_(εk) between the q-thiteration and the p-th iteration of step d), where q is an integerstrictly less than p, T is the duration in seconds of the time intervalwhich has elapsed between the q-th and the p-th iteration of step d). 3.The method as claimed in claim 1, in which the corrective factor is, inthe displacement law, added together or multiplied with the firstmeasured variable and the variation of the standard deviation σ_(α) ofthe predefined probability law is maintained below 10° per second formore than 90% of the time of use of the method for locating the device,the variation of the standard deviation σ_(α) being given by thefollowing ratio: Σσ_(αk)/T, where: σ_(αk) is the standard deviation ofthe predefined probability law during the k-th iteration of step d),Σσ_(αk) is the sum of the standard deviations σ_(αk) between the q-thiteration and the p-th iteration of step d), where q is an integerstrictly less than p, T is the duration in seconds of the time intervalwhich has elapsed between the q-th and the p-th iteration of step d). 4.The method as claimed in claim 1, in which, after several iterations ofsteps c) to e), the method comprises a step of re-sampling the particlesduring which: the particles associated with the lowest weights areeliminated, and new particles are automatically generated to replace theeliminated particles, a new current value of the corrective factor beingassigned to each new particle, each new value being dependent on one ormore of the corrective factor's current values associated with theparticles which have not been eliminated and independent of thecorrective factor's current values associated with the particles whichhave been eliminated.
 5. The method as claimed in claim 1, in which:during step a), the predefined constraints provided contain coordinatescoding the positions and the dimensions of obstacles which areimpassable to the device in the three-dimensional space, and step e)comprises, for each particle: the search for an intersection between thesegment [P^(i) _(k-1); P^(i) _(k)] and an impassable obstacle by usingthe coordinates of this impassable obstacle which are provided duringstep a), and the decreasing of the weight associated with the particleif such an intersection exists and, in the converse case, the absence ofdecreasing or the increasing of the weight associated with the particle.6. The method as claimed in claim 5, in which: during step a), the mapprovided contains several distinct zones, each distinct zone beingassociated: with coordinates defining the position on the map of itsperiphery, and a list of identifiers of just the impassable obstaclessituated inside this zone, step e) systematically comprises for eachparticle: an operation of identifying the zone inside which the particleis situated by comparing the updated coordinates of this particle withthe peripheries of the zones of the map which are defined by thecoordinates provided during step a), and then an operation of searchingfor an intersection between the segment [P^(i) _(k-1); P^(i) _(k)] andsolely the impassable obstacles whose identifiers are contained in thelist associated with the zone identified during the identificationoperation.
 7. The method as claimed in claim 1, in which: during stepa), the map provided contains several distinct zones, each distinct zonebeing associated: with coordinates defining the position on the map ofits periphery, and a displacement law from among a set of severaldifferent displacement laws, the displacement law associated with a zonemaking it possible to estimate more precisely, on the basis of the samemeasurements received, the direction and the amplitude of thedisplacement of the device when the latter is situated inside the zonethan if any one of the other displacement laws of the set were used, forthis purpose the different displacement laws are distinguished from oneanother by the mathematical operations which link the coordinates of aparticle to the measurements received during step c), and step d)systematically comprises for each particle: an operation of identifyingthe zone inside which the particle is situated by comparing thecoordinates of this particle with the peripheries of the zones of themap which are defined by the coordinates provided during step a), andthen an operation of use for the updating of the coordinates of theparticle of just the displacement law associated with the zoneidentified during the identification operation.
 8. The method as claimedin claim 1, in which: during step a), the map provided contains at leastone zone with favored direction of displacement associated: withcoordinates defining the position on the map of its periphery, and witha favored direction of displacement in this zone, step e) comprises foreach particle: an operation (94) of detecting the presence of theparticle inside the zone with favored direction of displacement bycomparing the coordinates of the particle with the periphery of the zonewith favored direction of displacement defined by the coordinatesprovided during step a), and then, if the particle is detected as beingpresent inside the zone with favored direction of displacement, anoperation of increasing the weight of this particle if the angulardeviation between the direction of displacement of this particle fromthe position P^(i) _(k-1) to the position P^(i) _(k) and the favoreddirection of displacement associated with this zone is equal to 0° or to180° to within plus or minus σ_(γ), the increasing being carried outwith respect to the weights of the other particles situated inside thesame zone and for which the deviation is not equal to 0° or to 180° towithin plus or minus σ_(γ), where σ_(γ) is a predetermined angulartolerance, and if the particle is detected as being outside of the zonewith favored direction of displacement, the prohibiting of the use ofthe favored direction of displacement associated with this zone toupdate the weight of the particle.
 9. An information recording medium,which comprises instructions for executing a method as claimed in claim1, when these instructions are executed by an electronic computer. 10.An electronic unit for locating a device displaceable inside athree-dimensional space, the electronic unit comprising: a memorycontaining a map of the three-dimensional space and predefinedconstraints on the displacements of the device in this three-dimensionalspace, an electronic computer programmed for: b) generating severaldistinct particles, each particle being associated: with coordinatescoding its position on the map, and with a weight representing theprobability that the device is situated at the site of the particle, c)receiving measurements representative of the direction of displacementof the device and of the amplitude of this displacement from itsprevious position, these measurements being carried out by sensorsonboard the displaced device, d) updating the coordinates of theposition of each particle as a function of the measurements received andof a predetermined displacement law for displacing the particle from itsprevious position P^(i) _(k-1) to a new position P^(i) _(k) in a mannercorrelated with the measured displacement of the device, eachdisplacement law comprising for this purpose at least one first measuredvariable whose value is dependent on the measurement of the direction ofdisplacement received and a second measured variable whose value isdependent on the measurement of the amplitude of the displacementreceived, e) for each particle, if the latest displacement of theparticle from the position P^(i) _(k-1) to the position P^(i) _(k)satisfies the predefined constraints, increasing the weight associatedwith the particle with respect to the weights of the particles whoselatest displacement infringes these predefined constraints, repeatingsteps c) to e), and f) estimating the position of the device on thebasis of the positions of the particles and of the weights associatedwith the particles by allotting, during this estimation, more importanceto the positions of the particles associated with the highest weights,wherein: the displacement law also comprises a corrective factor of abias combined with one of the measured variables by an arithmeticaloperation, and each particle is also associated with a current value ofthis corrective factor, the current value of this corrective factorbeing constructed at each iteration of step d) on the basis of aprevious current value of this corrective factor, computed during aprevious iteration of step d), to which is added a random variable drawnaccording to a predefined probability law, and the current values ofvarious particles being initialized, before the first execution of stepd), to various initial values, and the computer is programmed, for eachparticle whose coordinates are updated with the aid of the displacementlaw, to take the value of the corrective factor in the displacement lawequal to the corrective factor's current value associated with theparticle.
 11. A device directly transportable by a pedestrian who ismoving in displacement inside a three-dimensional space, the devicecomprising an inertial platform able to measure physical quantitiesrepresentative of the direction of displacement of the device and of theamplitude of the displacement, wherein the device also comprises anelectronic locating unit as claimed in claim 10.